The answer is 28 because you would use Pythagorean theorem
Answer:
The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
Step-by-step explanation:
From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).
The slope of the line is
m= y2-y1/x2-x1 = 10-5/4-2 = 5/2
The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.
Since the rate of change (slope) is same for all points, therefore the table represents a linear function.
If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.
Answer:
x=-3/7 and y=_23/7
Step-by-step explanation:
y=-4x-5 and y=3x-2
using comparison method
-4x-5=3x-2
-4x-3x=-2+5
-7x=3
x=3/-7
substituting the value of x
y=3x-2
=3×(-3/7)-2
=-9/7-2
=-9-14/7
=-23/7
Answer:
Allan can order them from least to greatest.
Step-by-step explanation:
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
